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GeoGebra Script: Rotating circles

Version 1: Polar form

s = Slider(0.1, 1.5, 0.01) t = Slider(0, 2pi, 0.01) n = Slider(0, 50, 1) Ln = 0...n LR = Zip(s^k, k, Ln) LP = Join({(0, 0)}, Zip((s^k * (1 - s); (k+1) * t), k, Ln)) LS = Zip(Sum(LP, k), k, Ln+1) LC = Zip(Circle(P, r), P, LS, r, LR)

Task:

You may like to explore what happens when s>1! Also, if you prefer, you can define the list LP considering the cartesian form. That is LP = Join( {(0,0)}, Zip((s^k * (1-s) * cos((k+1)t), s^k * (1-s) * sin((k+1)t)), k, Ln) ) It just a little bit longer, compared to the polar form.

Demo: Polar form

Version 2: Using complex numbers

r = Slider(0.1, 1.5, 0.01) t = Slider(0, 2pi, 0.01) n = Slider(0, 50, 1) Ln = 0...n Z = r * exp(i * t) LR = Zip(r^k, k, Ln) LP = Zip((1/r - 1) Z^k, k, Ln) LS = Zip((1-1/r, 0) + Sum(LP, k), k, Ln+1) LC = Zip(Circle(P, R), P, LS, R, LR)

Task:

Explore what happens when r>1!
If you make a different version, let me know: https://x.com/jcponcemath | ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄| Have ∞ fun!!!! |___________| (\__/) || (•ㅅ•) || /   づ